Global existence of Maxwell–Klein–Gordon fields in (2+1)-dimensional space-time

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Abstract
We study the global existence problem for the Maxwell–Klein–Gordonequations in (2+1)‐dimensional, Minkowski spacetime. We first establish local existence, in a suitable Sobolev space, by specializing to the Lorentz gauge and applying standard techniques. We then prove global existence by showing that an appropriate norm of the solutions cannot blow up in a finite time. An essential step in the proof involves showing that a certain second order ’’energy’’ does not blow up.

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